Solve -(b-a)-[-(a+2b-1)+(1/aab)]-sum3/2a+b=(1/2b+1)+1/aab

$$- ( b - a ) - [ - ( a + 2 b - 1 ) + ( \frac { 1 } { a } a b ) ] - \sum \frac { 3 } { 2 } a + b = ( \frac { 1 } { 2 } b + 1 ) + \frac { 1 } { a } a b$$

Solve for b

$$b=-3aΣ+4a-4$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2a, the least common multiple of a,2.

$$2a\left(-\left(b-a\right)-\left(-\left(a+2b-1\right)+\frac{1}{a}ab\right)-Σ\times \frac{3}{2}a\right)+2ab=\frac{1}{2}b\times 2a+2a+2\times 1ab$$

To find the opposite of b-a, find the opposite of each term.

$$2a\left(-b+a-\left(-\left(a+2b-1\right)+\frac{1}{a}ab\right)-Σ\times \frac{3}{2}a\right)+2ab=\frac{1}{2}b\times 2a+2a+2\times 1ab$$

To find the opposite of a+2b-1, find the opposite of each term.

$$2a\left(-b+a-\left(-a-2b+1+\frac{1}{a}ab\right)-Σ\times \frac{3}{2}a\right)+2ab=\frac{1}{2}b\times 2a+2a+2\times 1ab$$

Express \frac{1}{a}a as a single fraction.

$$2a\left(-b+a-\left(-a-2b+1+\frac{a}{a}b\right)-Σ\times \frac{3}{2}a\right)+2ab=\frac{1}{2}b\times 2a+2a+2\times 1ab$$

Cancel out a in both numerator and denominator.

$$2a\left(-b+a-\left(-a-2b+1+1b\right)-Σ\times \frac{3}{2}a\right)+2ab=\frac{1}{2}b\times 2a+2a+2\times 1ab$$

Combine -2b and 1b to get -b.

$$2a\left(-b+a-\left(-a-b+1\right)-Σ\times \frac{3}{2}a\right)+2ab=\frac{1}{2}b\times 2a+2a+2\times 1ab$$

To find the opposite of -a-b+1, find the opposite of each term.

$$2a\left(-b+a+a+b-1-Σ\times \frac{3}{2}a\right)+2ab=\frac{1}{2}b\times 2a+2a+2\times 1ab$$

Combine a and a to get 2a.

$$2a\left(-b+2a+b-1-Σ\times \frac{3}{2}a\right)+2ab=\frac{1}{2}b\times 2a+2a+2\times 1ab$$

Combine -b and b to get 0.

$$2a\left(2a-1-Σ\times \frac{3}{2}a\right)+2ab=\frac{1}{2}b\times 2a+2a+2\times 1ab$$

Multiply \frac{1}{2} and 2 to get 1.

$$2a\left(2a-1-Σ\times \frac{3}{2}a\right)+2ab=ba+2a+2\times 1ab$$

Multiply 2 and 1 to get 2.

$$2a\left(2a-1-Σ\times \frac{3}{2}a\right)+2ab=ba+2a+2ab$$

Combine ba and 2ab to get 3ba.

$$2a\left(2a-1-Σ\times \frac{3}{2}a\right)+2ab=3ba+2a$$

Subtract 3ba from both sides.

$$2a\left(2a-1-Σ\times \frac{3}{2}a\right)+2ab-3ba=2a$$

Combine 2ab and -3ba to get -ab.

$$2a\left(2a-1-Σ\times \frac{3}{2}a\right)-ab=2a$$

Subtract 2a\left(2a-1-Σ\times \frac{3}{2}a\right) from both sides.

$$-ab=2a-2a\left(2a-1-Σ\times \frac{3}{2}a\right)$$

Multiply -1 and \frac{3}{2} to get -\frac{3}{2}.

$$-ab=2a-2a\left(2a-1-\frac{3}{2}Σa\right)$$

Use the distributive property to multiply -2a by 2a-1-\frac{3}{2}Σa.

$$-ab=2a-4a^{2}+2a+3a^{2}Σ$$

Combine 2a and 2a to get 4a.

$$-ab=4a-4a^{2}+3a^{2}Σ$$

The equation is in standard form.

$$\left(-a\right)b=3Σa^{2}+4a-4a^{2}$$

Divide both sides by -a.

$$\frac{\left(-a\right)b}{-a}=\frac{a\left(3aΣ-4a+4\right)}{-a}$$

Dividing by -a undoes the multiplication by -a.

$$b=\frac{a\left(3aΣ-4a+4\right)}{-a}$$

Divide a\left(4-4a+3aΣ\right) by -a.

$$b=-3aΣ+4a-4$$

Solve for a

$$\left\{\begin{matrix}a=\frac{b+4}{4-3Σ}\text{, }&b\neq -4\text{ and }Σ\neq \frac{4}{3}\\a\neq 0\text{, }&b=-4\text{ and }Σ=\frac{4}{3}\end{matrix}\right.$$